The following preprint is available: Limits in double categories by Marco Grandis and Robert Pare Abstract. We define the notion of (horizontal) double limit for a double functor F: I -> A between double categories, and we give a construction theorem for such limits, from double products, double equalisers and tabulators (the double limits of vertical arrows). Double limits can describe important tools; for instance, the Grothendieck construction of a profunctor is its tabulator, in the "double category" of categories, functors and profunctors. If A is a 2-category, the previous result reduces to Street's construction theorem of weighted limits, by ordinary limits and cotensors 2*X (the tabulator of the vertical identity of the object X). Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.10.353 6805 fax: +39.10.353 6752 home page: http://www.dima.unige.it/STAFF/GRANDIS/